Problem: Solve for $x$ and $y$ using elimination. ${4x+3y = 42}$ ${-x+2y = 17}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${4x+3y = 42}$ $-4x+8y = 68$ Add the top and bottom equations together. $11y = 110$ $\dfrac{11y}{{11}} = \dfrac{110}{{11}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {4x+3y = 42}\thinspace$ to find $x$ ${4x + 3}{(10)}{= 42}$ $4x+30 = 42$ $4x+30{-30} = 42{-30}$ $4x = 12$ $\dfrac{4x}{{4}} = \dfrac{12}{{4}}$ ${x = 3}$ You can also plug ${y = 10}$ into $\thinspace {-x+2y = 17}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(10)}{= 17}$ ${x = 3}$